Completing a2×2Block Matrix of Real Quaternions with a Partial Specified Inverse

[摘要] This paper considers a completion problem of a nonsingular2×2block matrix over the real quaternion algebraℍ: Letm1,  m2,  n1,  n2be nonnegative integers,m1+m2=n1+n2=n>0, andA12∈ℍm1×n2, A21∈ℍm2×n1, A22∈ℍm2×n2, B11∈ℍn1×m1be given. We determine necessary and sufficient conditions so that there exists a variant block entry matrixA11∈ℍm1×n1such thatA=(A11A12A21A22)∈ℍn×nis nonsingular, andB11is the upper left block of a partitioning ofA-1. The general expression forA11is also obtained. Finally, a numerical example is presented to verify the theoretical findings.

[学科分类] 应用数学